Inference for multi-dimensional high-frequency data: Equivalence of methods, central limit theorems, and an application to conditional independence testing

Markus Bibinger and Per A. Mykland

No 2013-006, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous. The central limit theorem is shown to have a feasible version. In the process, we show that the classes of multi-scale and kernel estimators for smoothing noise perturbation are asymptotically equivalent in the sense of having the same asymptotic distribution for corresponding kernel and weight functions. We also include the analysis for the Hayashi-Yoshida estimator in absence of microstructure. The theory leads to multi-dimensional stable central limit theorems for respective estimators and hence allows to draw statistical inference for a broad class of multivariate models and linear functions of the recorded components. This paves the way to tests and confidence intervals in risk measurement for arbitrary portfolios composed of high-frequently observed assets. As an application, we enhance the approach to cover more complex functions and in order to construct a test for investigating hypotheses that correlated assets are independent conditional on a common factor.

Keywords: asymptotic distribution theory; asynchronous observations; conditional independence; high-frequency data; microstructure noise; multivariate limit theorems (search for similar items in EconPapers)
JEL-codes: C14 C32 C58 G10 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/79571/1/734349017.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb649:sfb649dp2013-006

Access Statistics for this paper

More papers in SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().